WEAK INTERACTIONS IN A BACKGROUND OF A UNIFORM MAGNETIC FIELD. A MATHEMATICAL MODEL FOR THE INVERSE β DECAY.I.
Résumé
In this paper we consider a mathematical model for the inverse $\beta$ decay in a uniform magnetic field. With this model we associate a Hamiltonian with cutoffs in an appropriate Fock space. No infrared regularization is assumed. The Hamiltonian is self-adjoint and has a unique ground state. We study the essential spectrum and determine the spectrum. The coupling constant is supposed sufficiently small.
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